There is a small air bubble inside a glass sphere (\( \mu = 1.5 \)) of radius 10 cm. The bubble is 4.0 cm below the surface and is viewed normally from outside as shown. The apparent depth of the bubble will be

A metal plate is getting heated. It can be because of:
A. An alternating current is passing through the plate.
B. It is placed in a time varying magnitude field.
C. A direct current is passing through the plate.
D. It is placed in a space varying magnitude field, but does not vary with time.
E. It is placed in a time constant magnetic filed.
Choose the correct answer from the options given below:

A proton of charge \(1.6 \times 10^{-19} C\) is moving with a velocity of \(5 \times 10^3 m / s\) in a magnetic field of 4 T. The work done by the magnetic field on the proton is :

One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).
What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?

In photoelectric effect, the stopping potential depends on the

In the given circuit, the resistance of the galvanometer is \( G = 100 \text{ } \Omega \). Resistance box R contributes \( 4900 \text{ } \Omega \). When key K is closed. The needle of the galvanometer deflects to the 20th division. The figure of merit of the galvanometer is:

A battery has an e.m.f 12 V and internal resistance 2 \(\Omega\) This battery is connected to a variable resistor 0 to 5 \(\Omega\). The value of current for which the rate of heat production in the resistor is maximum:

In the given complexes, the heteroleptic complexes is/are:
A. \(\left[ Co \left( NH _3\right)_6\right]^{3+}\)
B. \(\left[ Cr \left( H _2 O \right)_6\right]^{3+}\)
C. \(\left[ Ni ( Cl )_2\left( PPh _3\right)_2\right]\)
D. \(\left[ Co \left( NH _3\right)_4 Cl _2\right]^{+}\)
Choose the correct answer from the options given below:

If for the following data :

YEAR (X)	2000	2001	2002	2003	2004	2005	2006
PRODUCTION (iN TONNES) (Y)	40	45	46	42	47	50	46

the equation of the straight line trend is \(y=45.143+1.036(x-2003)\), then the trend value for the year 2004 is

Let \(\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}\), and \(\vec{c}=2 \hat{i}+\hat{j}+4 \hat{k}\).
A vector \(\vec{d}\) which is perpendicular to both \(\vec{a}\) and \(\vec{b}\) and satisfies \(\vec{c} \cdot \vec{d}=14\) is :

For the matrix \(A=\left[\begin{array}{ll}3 & 1 \\ 7 & 5\end{array}\right], 8 A^{-1}=\) ‾‾‾‾‾‾‾‾‾‾

Read the passage and answer the question given below.
When a host is exposed to antigens, which may be in the form of living or dead microbes or other proteins, antibodies are produced in the host body. This type of immunity is called active immunity. Active immunity is slow and takes time to give its full effective response. Injecting the microbes deliberately during immunisation or infectious organisms gaining access into body during natural infection induce active immunity. When antibodies are directly given to protect the body against foreign agents, it is called passive immunity.
Immunity provided to the foetus from the mother through placenta during pregnancy is :

Match List - I with List - II.

List - I	List - II
(A) Cloning vector	(I) Sea weeds
(B) β-galactosidase	(II) Selectable marker
(C) Agarose	(III) Ti-plasmid of Agrobacterium tumifaciens
(D) \(a m p^{ R }\) in pBR322	(IV) Chromogenic screening

Choose the correct answer from the options given below :